where \(Q\)  is the QFI matrix and \(N\)  is the number sites. The threshold for genuine multipartite entanglement is then given (in the thermodynamic limit) by \(\bar{f} > 3mA\)  where \(A\)  is the metric constant. The bound in [1]} can be recovered for the choice of \(A=4\)  which corresponds to the QFI most used in a physics context. The trace on the right hand side of Eq. REF  can be arrived at by considering the operator defined in Eq. REF  and then integrating over all possible orientations of the unit vectors (for fixed relative orientations).
